Every page has its own value for a TV. It the page value matches the default value, the page value is not set (because the default value will be used when it's empty).
If you manually enter the value of a TV for a specific page, that's the value for that page from then on, regardless of what you do to the TV. The only exceptions are changing the template or deleting the TV.
Because of the way it works, it's really best to think of the TV's default value as only applying when you create a new page.
That said, it often works well to set the TV to:
That way it will inherit any page value set in an ancestor but get "some_value" if no ancestor has a page value for the TV.